Perturbation methods, solvation

CALCULATION OF SOLVATION ENERGIES BY FREE-ENERGY PERTURBATION METHODS... 

Consider the application of the quantum mechanical perturbation method to the analysis of interaction of systems R and S. The total perturbation energy from such an interaction is comprised of contributions from neighbouring effects resulting in ion-pair formation without electron transfer and partial charge transfer due to covalent bonding. This approach also takes into account solvation effects. 

Bash et al. (1987) applied the thermodynamic perturbation method to complexes of thermolysin with a phosphonamidate [Cbz-Gly -(NH)-Leu-Leu] and the corresponding phosphonate inhibitor [Cbz-Gly -(0)-Leu-Leu]. The perturbation was carried out by using 20 windows, with 2-psec molecular dynamics simulations in each window. Computations were for the ligand in solution and bound to the enzyme. The solvation of the enzyme was represented by a spherical cap of 168 water molecules about the bound inhibitor. The difference in free energy of binding of the two inhibitors was calculated to be 4.38 kcal/mol, to be compared with the experimental value, 4.10 kcal/mol. These calculations point out the importance of solvation effects, which are seen in the 3.4 kcal/mol difference between the NH and O forms of the inhibitor. 

Simulations, Time-dependent Methods and Solvation Models 16.1 Simulation Methods 16.1.1 Free Energy Methods 16.1.2 Thermodynamic Perturbation Methods 16.1.3 Thermodynamic Integration Methods 16.2 Time-dependent Methods ill 373 380 380 381 383 ... 

Ewing, P. J. and T. P. Lybrand. (1993). A comparison of perturbation method and PB electrostatic calculations for estimation of relative solvation free energies. J. Phys. Chem. 98 1748-52. 

Further developments of these ideas took place in computational structural biology, where nonphysical local transformations were implemented within the framework of thermodynamic cycles. These nonphysical transformations were introduced in 1981 by Warshel, who studied ionization in acidic residues in proteins pK calculations). Although the cycle included nonphysical transformations, they were not carried out by the perturbation technique. A year later Warshel used the perturbation method together with umbrella sampling to study the solvation free energy contribution to an electron transfer reaction coordinate, using two spheres for donor and acceptor in water the perturbation, however, was performed along a physical path. Warshel also modeled some enzymatic reactions that involve nonphysical processes. ... 

M. R. Reddy and M. D. Erion, J. Comput. Chem., 20,1018 (1999), Calculation of Relative Solvation Free Energy Differences by Thermodynamic Perturbation Method Dependence of the Free Energy Results on the Simulation Length. 

We introduce here one more extremely useful molecular mechanics based technique perturbation methods. Although somewhat advanced, the method is so powerful that students of modem organic chemistry should know of it. The fact is that the explicit solvation methods only became really meaningful for experimentalists when the perturbation methods discussed here were introduced. We will provide only a very brief introduction. Note the method is equally compatible with MC and MD methods. 

AMI COSMO and COSMO-RS Hydrogen Bonding 1 Hydrogen Bonding 2 Intermolecular Interactions by Perturbation Theory MNDO PM3 Self-consistent Reaction Field Methods Solvation Modeling Water Clusters,... 

It is often the case that the solvent acts as a bulk medium, which affects the solute mainly by its dielectric properties. Therefore, as in the case of electrostatic shielding presented above, explicitly defined solvent molecules do not have to be present. In fact, the bulk can be considered as perturbing the molecule in the gas phase , leading to so-called continuum solvent models [14, 15]. To represent the electrostatic contribution to the free energy of solvation, the generalized Bom (GB) method is widely used. Wilhin the GB equation, AG equals the difference between and the vacuum Coulomb energy (Eq. (38)) ... 

The SPARC (Sparc Performs Automated Reasoning in Chemistry) approach was introduced in the 1990s by Karickhoff, Carreira, Hilal and their colleagues [16-18]. This method uses LSER [19] to estimate perturbed molecular orbitals [20] to describe quantum effects such as charge distribuhon and delocalizahon, and polarizability of molecules followed by quanhtative structure-activity relationship (QSAR) studies to correlate structure with molecular properties. SPARC describes Gibbs energy of a given process (e.g. solvation in water) as a sum of ... 

Tables 11-6, 11-7, and 11-8 show calculated solvatochromic shifts for the nucle-obases. Solvation effects on uracil have been studied theoretically in the past using both explicit and implicit models [92, 94, 130, 149, 211-214] (see Table 11-6). Initial studies used clusters of uracil with a few water molecules. Marian et al. [130] calculated excited states of uracil and uracil-water clusters with two, four and six water molecules. Shukla and Lesczynski [122] studied uracil with three water molecules using CIS to calculate excitation energies. Improta et al. [213] used a cluster of four water molecules embedded into a PCM and TDDFT calculations to study the solvatochromic shifts on the absorption and emission of uracil and thymine. Zazza et al. [211] used the perturbed matrix method (PMM) in combination with TDDFT and CCSD to calculate the solvatochromic shifts. The shift for the Si state ranges between (+0.21) - (+0.54) eV and the shift for the S2 is calculated to be between (-0.07) - (-0.19) eV. Thymine shows very similar solvatochromic shifts as seen in Table 11-6 [92],...

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